Hysteresis is one of key factors influencing the output of magnetorheological (MR) actuators. The actuators reveal two primary sources of hysteresis. The hydro(mechanical) hysteresis can be related to flow dynamics mechanisms and is frequency- or rate-dependent. For comparison, the magnetic hysteresis is an inherent property of ferromagnetic materials forming the magnetic circuit of the actuators. The need for a good quality hysteresis model has been early recognized in studies on MR actuators; however, few studies have provided models which could be used in the design stage. In the paper we reveal a hybrid multiphysics model of a flow-mode MR actuator which could be used for that purpose. The model relies on the information which can be extracted primarily from material datasheets and engineering drawings. We reveal key details of the model and then verify it against measured data. Finally, we employ it in a parameter sensitivity study to examine the influence of magnetic hysteresis and other relevant factors on the output of the actuator.